Evaluation of Approaches for Tracking Virus
Particles in Fluorescence Microscopy Images
W. J. Godinez1, M. Lampe2, S. W¨ orz1, B. M¨ uller2, R. Eils1, K. Rohr1
1University of Heidelberg, BIOQUANT, IPMB, and DKFZ Heidelberg,
Dept. Bioinformatics and Functional Genomics, Biomedical Computer Vision Group,
Im Neuenheimer Feld 267, 69120 Heidelberg, Germany
2University of Heidelberg, Dept. of Virology,
Im Neuenheimer Feld 324, 69120 Heidelberg, Germany
Abstract. Tracking virus particles in fluorescence microscopy image se-
quences enables the characterization of the dynamical behavior of these
objects. Several approaches have been developed for the task of virus
tracking. However, few studies have quantitatively evaluated the per-
formance of the different approaches. Such a comparison is essential to
predict the performance of the approaches under realistic conditions. In
this paper, we present a quantitative evaluation of eight approaches for
tracking virus particles. We have investigated deterministic and prob-
abilistic approaches. The evaluation is based on nine real microscopy
image sequences of virus particles, for which ground truth was obtained
by manual tracking.
Tracking single virus particles in fluorescence time-lapse microscopy images
yields quantitative information that describes their dynamical behavior. Such
information can be employed to characterize the influence of antiviral drugs.
To obtain statistically sound conclusions, a large number of particles must be
tracked. Therefore, automatic tracking approaches are required to efficiently
handle the large amount of image data.
Several approaches for virus tracking have been described. Typically, deter-
ministic approaches have been employed (e.g., [1, 2]). More recently, probabilis-
tic approaches (e.g., [3, 4]) have been introduced. However, few studies have
quantitatively compared the performance of virus tracking approaches. Such
a comparison is needed to predict the performance of the approaches for real
images. The most detailed comparison of tracking approaches for fluorescent
particles has been presented in . There, the authors evaluate the perfor-
mance of four deterministic tracking approaches using synthetic images with
a focus on object localization. One main finding is that the performance of
the tracking approaches declines as the signal-to-noise ratio (SNR) decreases.
While the study is relatively detailed, it has three shortcomings. First, the per-
formance measure is based on the localization error, and the influence of errors
208 Godinez et al.
in correspondence finding is ignored. Second, no real images have been used.
Third, only deterministic approaches are considered.
In this work, we present a quantitative performance evaluation of approaches
for tracking multiple virus particles in microscopy image sequences. In total, we
have evaluated eight tracking approaches. We have analyzed two deterministic
approaches as well as six probabilistic approaches. The deterministic approaches
are based on either the spot-enhancing filter  or 2D Gaussian fitting for particle
localization, and a global nearest neighbor approach for motion correspondence.
The probabilistic approaches are based on Kalman filters, mixture of particle
filters (MPF), and independent particle filters (IPF). The approaches have been
applied to synthetic image sequences displaying virus-like objects, as well as to 9
different real microscopy image sequences (each comprising between 150 and 400
frames) displaying HIV-1 particles. In comparison to , the employed perfor-
mance measure reflects more comprehensively the performance of the evaluated
2 Materials and methods
2.1 Deterministic tracking approaches
The deterministic approaches follow a two-step paradigm consisting of object
localization and motion correspondence. For object localization, we employed
two approaches: an approach based on the spot-enhancing filter (SEF), and an
approach using 2D Gaussian fitting (GaussFit). For motion correspondence, we
used a global nearest neighbor (GNN) approach . By combining the localiza-
tion schemes with the motion correspondence scheme we obtain two deterministic
approaches: 1) spot-enhancing filter with global nearest neighbor (SEF&GNN),
and 2) 2D Gaussian fitting with global nearest neighbor (GaussFit&GNN).
2.2 Probabilistic tracking approaches
The probabilistic approaches follow a Bayesian paradigm, where the aim is to
estimate the state xtof a virus particle at time step t given a sequence of mea-
surements y1:t. A solution to this problem involves computing the posterior
distribution p(xt|y1:t) using stochastic propagation and Bayes’ theorem:
p(xt|y1:t) ∝ p(yt|xt)p(xt|y1:t−1).
Given certain assumptions on the form of the distributions, the recursion can
be solved analytically using a Kalman filter. More generally, the recursive re-
lation can be solved via approximation using a particle filter. The idea behind
this filter is to approximate the posterior distribution using a set of weighted
random samples. When tracking multiple objects, multiple modes arise in the
posterior distribution. The multimodality can be modeled via a non-parametric
M-component mixture model, which can be computed using a mixture of parti-
cle filters . Alternatively, one may track multiple objects by instantiating one
Evaluation of Approaches for Tracking Virus Particles 209
independent particle filter per object (e.g., ). To prevent the problem of filter
coalescence, the IPF includes a penalization scheme . Similarly, one may use
one Kalman filter per object to track multiple objects.
For all probabilistic approaches, we employed the two localization schemes de-
scribed above to detect virus particles. Note that the approaches using a mixture
of particle filters can only track a fixed number of objects. For the approaches
using independent particle filters and Kalman filters, the motion correspondence
problem, i.e., the problem of assigning the position measurements computed
by the localization schemes to each spatial-temporal filter, is addressed using
a global nearest neighbor approach. The combination of the two localization
algorithms with the different filters yields the following tracking approaches: 3)
spot-enhancing filter and Kalman filters (SEF&Kalman), 4) spot-enhancing fil-
ter and a mixture of particle filters (SEF&MPF), 5) spot-enhancing filter and
independent particle filters (SEF&IPF), 6) 2D Gaussian fitting and Kalman fil-
ters (GaussFit&Kalman), 7) 2D Gaussian fitting and a mixture of particle filters
(GaussFit&MPF), and 8) 2D Gaussian fitting and independent particle filters
To quantitatively assess the performance of each approach in each image se-
quence, we have employed the tracking accuracy Ptrack=
flects the ratio between the number of correctly computed trajectories ntrack,correct
and the number of true trajectories ntrack,total. The value ntrack,correctis com-
puted as the weighted sum of the percentage of tracked time steps rtracked,i
for each i-th true trajectory: ntrack,correct =?ntrack,total
the number of correctly computed trajectories ntrack,icorresponding to each i-th
true trajectory: wi= G(ntrack,i;µ = 1,σ = 1). The weighting scheme is intro-
duced to penalize computed trajectories that are broken. A computed trajectory
is assumed to be correct if the Euclidean distance between the measured object
position and the true object position is below 2 pixels.
ntrack,total, which re-
wirtracked,i, where the
weight wi is given by a Gaussian function G(·), which takes as its argument
We have applied all eight approaches to synthetic as well as real microscopy
images. Below, we present the results for nine real microscopy image sequences.
In these sequences, fluorescently labeled HIV-1 particles were imaged using a
fluorescence wide-field microscope; movies were recorded with a frequency of
10Hz. Ground truth for the virus positions was obtained by manual tracking
using the commercial software MetaMorph. For all sequences, we have employed
fixed parameter values for all approaches. Similarly, the noise parameters for the
dynamical model of the Kalman filter were set analogously as the ones employed
for the particle filter. Details for each sequence are given in Table 1. The quan-
titative experimental results for the nine sequences are presented in Table 2. As
an example, results for the real image sequence “Seq. 7” are shown in Fig. 1.
210Godinez et al.
Table 1. Description of real microscopy image sequences.
No. of time steps No. of objects
Table 2. Tracking accuracy Ptrack for real microscopy image sequences.
SEF& SEF& SEF& SEF& GaussFit& GaussFit& GaussFit& GaussFit&
GNN Kalman MPF IPFGNNKalman MPFIPF
Std. Dev. 13.68
Our experimental results in Table 2 indicate that the performance of the deter-
ministic approaches is not very good (e.g., for the best deterministic approach,
namely SEF&GNN, we obtain a mean tracking accuracy of¯Ptrack= 67.33%).
The reason for this is that localization errors (e.g., detection failures) as well
as errors in correspondence finding (e.g, incorrect assignments) reduce the num-
ber of correctly computed trajectories. The approaches based on the Kalman
filter, in comparison to the deterministic approaches, yield an improved per-
formance (e.g.,¯Ptrack = 72.93% for the best Kalman-based approach, namely
SEF&Kalman). This suggests that the inclusion of a spatial-temporal filter-
ing step enhances the performance. For the approaches using particle filters, it
turned out that those using independent particle filters (IPF) outperform those
using a mixture of particle filters (MPF). The reason for this result is twofold:
Evaluation of Approaches for Tracking Virus Particles 211
Fig.1. Tracking results for four approaches for the real image sequence“Seq. 7”(time
step t = 110).
(a) SEF&GNN(b) SEF&Kalman(c) SEF&MPF (d) SEF&IPF
first, MPF cannot track a variable number of objects (whereas in the real images,
the number of objects varies over time); second, the MPF uses a variable number
of samples to estimate each mixture component. As such, the estimation accu-
racy decreases for those components for which few samples have been assigned.
Among all approaches, the best tracking accuracy is obtained by GaussFit&IPF
(¯Ptrack= 78.74%). The superior performance is mainly due to the comprehen-
sive tracking machinery of the particle filter, which includes the steps of particle
localization, motion correspondence, and position estimation. In summary, the
quantitative results suggest that the probabilistic approaches are more accurate
than the deterministic schemes.
Acknowledgement. Support of the BMBF (FORSYS) project VIROQUANT
is gratefully acknowledged.
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